This week it was wizard online crime maps, last month a new "public data corporation". Barely a day seems to go by without some new torrent of data bursting from Whitehall as part of David Cameron's crusade to become "the most open and transparent government in the world".

A brief tour of government websites reveals a frenzy of transparent activity: at data.gov.uk I can find out from the transparently published minutes of the Transparency Board that on 11 January "the Cabinet Office transparency team presented Paper TB(4)3 to the Transparency Board" on the development of a "transparency vision". And that progress on the "Short Term Transparency Data Publication Plan is generally encouraging".

All of which is not to be scoffed at. The publication of industrial amounts of data on spending, public sector pay and government contracts are genuinely radical steps towards a more open kind of government. Downing Street's determination to release the information in a digitally savvy and accessible form is equally admirable.

But the prime minister's enthusiasm for transparency is not, it seems, boundless.

For more than two weeks the Guardian has been trying to establish a few details about an evening Cameron spent at the Oxfordshire home of Rebekah Brooks, chief executive of News International, during the Christmas holidays. Here's what the most open government in the world told us: first, No 10 categorically denied the PM had visited Brooks on Christmas day itself; then, when we asked instead if the PM had been entertained chez Brooks over the Christmas period it declined to confirm or deny.

Later Downing Street elaborated on its position, pointing out that Brooks was a constituent of Cameron's and, in any case, "the prime minister regularly meets newspaper executives from lots of different companies". But still No 10 refused to provide a date, or even confirm whether the dinner took place.

When it emerged that James Murdoch was at the dinner too, Downing Street became fractionally more transparent: an unattributable source reassured lobby reporters that neither Rupert Murdoch's controversial takeover bid for Sky nor the phone-hacking scandal had been discussed. So that's all right then.

You don't have to be a conspiracy theorist to think a little more information would be useful to make up your mind whether there was anything untoward about the Brooks-Cameron soiree. So most days this week my colleague Caroline Davies called No 10 and asked the same questions. On what date did the dinner take place? Who was present? (According to some reports the guest list included Andy Coulson and Jeremy Clarkson.) Was the position of Coulson, then No 10 PR director, discussed? What days did the PM spend in his constituency over Christmas? And, just to be crystal clear, were either the Sky bid or phone-hacking discussed?

Cameron's position boils down to: "It was a private meeting so I don't have to tell you anything about it." But the border between public and private is more complicated if you're a senior politician. Imagine if the PM had had a private dinner with Hosni Mubarak. We'd consider that we had a right to know about it as we would quite understandably wonder if it had coloured the government's policy towards Cairo.

"Not only must justice be done," goes the old legal maxim. "It must also be seen to be done." The same holds for probity in government.

Cameron seemed to acknowledge as much in his introduction to the ministerial code which exhorted his government in all its behaviour, including "the meetings we hold", to "remember that we are not masters but servants".

The trouble is that we have no shortage of reasons to be suspicious about what really happened around Brooks's dinner table. Long before they tucked into the starters there was something whiffy about the relationship between No 10 and News International: why did the prime minister stand by his PR man long after most sentient people had concluded that his denials of involvement in phone-hacking were risible? Why were no minutes taken when Rupert Murdoch became one of Cameron's first visitors in No 10 ... or when the culture secretary, Jeremy Hunt, met James Murdoch shortly after Murdoch père launched his bid for full ownership of Sky?

Why is Downing Street refusing to disclose what date the Brooks dinner took place? Would people feel differently about it if, for instance, it happened on Boxing Day or Christmas Eve? Would that imply a level of intimacy that seemed a bit, well, odd? Labour's shadow culture secretary, Ivan Lewis, has been trying manfully to find out a little more about the Cameron-Brooks dinner, though his leader is somewhat less inclined to ruffle News International feathers.

Perhaps the new Downing Street communications director, Craig Oliver, will persuade his boss to extend his transparency crusade to this issue. Otherwise Cameron's exhortation that "together we can set a great example of what a modern democracy ought to look like" might ring a little hollow.